A metal crystallizes in two cubic phases, face-centred cubic and body-centred cubic, which have unit cell lengths `3.5 Å` and `3.0 Å`, respectively. Calculate the ratio of densities of fcc and bcc.

Options

A. `2.123`
B. `1.259`
C. `5.124`
D. `3.134`

Answer

b

Explanation

` rho = (n + M_(m))/(N_(A) xx a^(3))`
For fcc centred cubic cell `n = 4, a= 3.5 Å`
`rho(fc c) = (4 xx M_(m))/(N_(A) xx (3.5)^(3))`.....(i)
For bcc lattic `n= 2, a = 3.0 Å`
`rho (fc c) = (2 xx M_(m))/(N_(A) xx (3.0)^(2))`.....(ii)
from equation (i) and (ii)
`(rho(fc c))/(rho(fc c)) = (4)/(2) = (3^(2))/((1..5)^(2)) = (6 xx 3 xx 3)/(2 xx 3.5 xx 3.5 xx 3.5) = 1.259`